let n be Nat; :: thesis: for K being Field

for M1 being Matrix of n,K st M1 is Orthogonal holds

(M1 @) * M1 = M1 * (M1 @)

let K be Field; :: thesis: for M1 being Matrix of n,K st M1 is Orthogonal holds

(M1 @) * M1 = M1 * (M1 @)

let M1 be Matrix of n,K; :: thesis: ( M1 is Orthogonal implies (M1 @) * M1 = M1 * (M1 @) )

assume A1: M1 is Orthogonal ; :: thesis: (M1 @) * M1 = M1 * (M1 @)

then (M1 @) * M1 = 1. (K,n) by Th42;

hence (M1 @) * M1 = M1 * (M1 @) by A1, Th41; :: thesis: verum

for M1 being Matrix of n,K st M1 is Orthogonal holds

(M1 @) * M1 = M1 * (M1 @)

let K be Field; :: thesis: for M1 being Matrix of n,K st M1 is Orthogonal holds

(M1 @) * M1 = M1 * (M1 @)

let M1 be Matrix of n,K; :: thesis: ( M1 is Orthogonal implies (M1 @) * M1 = M1 * (M1 @) )

assume A1: M1 is Orthogonal ; :: thesis: (M1 @) * M1 = M1 * (M1 @)

then (M1 @) * M1 = 1. (K,n) by Th42;

hence (M1 @) * M1 = M1 * (M1 @) by A1, Th41; :: thesis: verum